Problem: $9tu - 6tv - 7t - 1 = -10u + 5$ Solve for $t$.
Combine constant terms on the right. $9tu - 6tv - 7t - {1} = -10u + {5}$ $9tu - 6tv - 7t = -10u + {6}$ Notice that all the terms on the left-hand side of the equation have $t$ in them. $9{t}u - 6{t}v - 7{t} = -10u + 6$ Factor out the $t$ ${t} \cdot \left( 9u - 6v - 7 \right) = -10u + 6$ Isolate the $t$ $t \cdot \left( {9u - 6v - 7} \right) = -10u + 6$ $t = \dfrac{ -10u + 6 }{ {9u - 6v - 7} }$ We can simplify this by multiplying the top and bottom by $-1$. $t= \dfrac{10u - 6}{-9u + 6v + 7}$